Microcapillary networks

ABSTRACT

Devices that include hosts having internal microcapillary networks are disclosed. The microcapillary networks are formed from interconnected passageways. The interconnected passageways may be formed by removing a fugitive material from a cured host material that forms the host. The resultant host material has many applications, including use as a microfluidic device in applications ranging from fluid mixing to structural repair.

REFERENCE TO PRIOR APPLICATION

[0001] This application claims the benefit of U.S. ProvisionalApplication No. 60/413,985, entitled “Microcapillary Networks,” filed onSep. 26, 2002, which is hereby incorporated by reference herein in itsentirety.

FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] This application was funded in part under the following researchgrants and contracts: AFOSR Aerospace and Materials Science DirectorateGrant No. F49620-00-1-0094 and NSF DMI Grant No. 00-99360. The U.S.Government may have rights in this invention.

BACKGROUND

[0003] Microchannel networks can include a multitude of interconnectedpassageways. These microchannel networks are often used in microfluidicsystems. A more complete description of microchannel networks and theirapplication in microfluidic devices may be found in Anderson, J. A., etal., Fabrication of topologically complex three-dimensional microfluidicsystems in PDMS by rapid prototyping. Anal. Chem. 74, 3158-64 (2000).

[0004] Conventional microchannel devices are constructed by multiplemethods, including laser machining, laser chemical processing,sacrificial wax, soft lithography, photopatterning, fused deposition,and two-photon polymerization. Two-dimensional microchannel devices aregenerally made by photolithographic or soft lithographic techniques andare limited to patterns on a flat surface, or at most a few stackedlayers. Forming these devices requires repetitive lithographicprocessing, in which each layer requires a separate mask or stamp.Multiple series of plates may be joined to form structures having a fewvertical layers.

[0005] These devices are made by etching open troughs into separateplates. Due to the limitations of lithography, the sidewalls of theetched troughs are straight. These plates are then joined, such as withan adhesive, so the open troughs align to form closed microchannelshaving square or rectangular internal shapes.

[0006] The approximately 90° corners of the square or rectangularmicrochannels provide many locations for stress cracks to form due tostress concentration at the corners. Since structures incorporatinglithographically formed microchannels have a tendency to crack, squareor rectangular microchannels are unsuitable for use in structuralcomposite materials. Furthermore, structural materials, such as epoxybased materials, cannot generally be etched using lithographic methods.

[0007] In addition to these square or rectangular microchannelsweakening materials in which they are incorporated, the corners provideareas for solids to collect. In this fashion, when colloids or othersolid containing fluids are passed through the device, some of thesolids collect in the corners. This build up of solids can result indecreased fluid movement through the device, in addition to plugging.

[0008] There is a need for self-healing structural materials. Structuralthermosetting polymers and fiber reinforced polymer composites, whichare used in a wide variety of applications ranging from microelectronicsto composite aircraft structures, such as fuselages, wings, and rotors,are susceptible to damage in the form of cracking. These cracks can formdeep within the structure where detection is difficult and repair isvirtually impossible.

[0009] Conventional self-healing or self-sealing materials use amicroencapsulated healing agent and a dispersed catalyst inside apolymer matrix to repair themselves. These self-healing materials areable to recover approximately 75% of the toughness of the originalmaterial prior to cracking. However, the use of these materials islimited because they can deliver the healing agent into the crack planeonly once.

[0010] In addition to improved self-healing materials, there is a needto exert greater control over fluid flow and mixing in microchanneldevices. Control over fluid flow and mixing is difficult in microfluidicdevices because laminar flow and diffusive mixing are the dominantmixing modes. These problems are of particular concern for mixing fluidsthat contain biological or other large molecules, such as DNA orproteins, because such species diffuse slowly. In these devices,prohibitively long path lengths are often required to ensure completemixing of the fluid constituents.

[0011] To reduce the planar footprint of such devices, recent effortshave focused on various design strategies for fluid mixing based onchaotic advection. Chaotic advection is believed to promote rapidstretching and folding of the fluid interfaces that are believed toexist within complex fluid flow patterns. A more detailed description ofchaotic advection can be found in Aref, H., “The development of chaoticadvection.” Phys. Fluids 14, 1315-25 (2002).

[0012] It is believed that chaotic advection is created in a fluid flowby either causing unsteadiness in the rate of fluid flow, or byproviding geometrically complex channels to direct the fluid. Byexploiting this phenomenon on the micro-scale, the interfacial surfacearea across which diffusion occurs is thought to greatly increase. Priorstrategies of fabricating microfluidic devices believed capable ofchaotic advection include fluid direction channels having “twisted pipearchitectures” and devices having bas-relief structures imprinted alongthe floor of the fluid direction channels. While these methods mayresult in enhanced mixing, the complexity of the devices is limited dueto the planar nature of the devices and the rectangular featuresobtained.

[0013] As can be seen from the above description, there is an ongoingneed for simple and efficient materials and methods for formingmicrochannel-type devices, including microfluidic devices used formixing and materials with the ability to self-heal. The microcapillarydevices, fabrication methods, and materials of the present inventionovercome one or more of the disadvantages associated with conventionaldevices.

SUMMARY

[0014] In one aspect, a device including a host having at least one,hollow, interconnected passageway is disclosed. The passageway has anaverage diameter from 0.1 micron to 1000 microns and is substantiallytubular in shape. Methods of forming this host by removing a fugitivematerial from a cured host material are also disclosed.

[0015] In another aspect, a host having internal, vertically-oriented,square-spiral mixing towers is disclosed.

[0016] In another aspect, a method of closing an opening in an articleis disclosed.

[0017] In another aspect, a method of mixing a fluid is disclosed.

[0018] Other systems, methods, features and advantages of the inventionwill be, or will become, apparent to one with skill in the art uponexamination of the following figures and detailed description. It isintended that all such additional systems, methods, features andadvantages be included within this description, be within the scope ofthe invention, and be protected by the following claims.

BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The invention can be better understood with reference to thefollowing drawings and description. The components in the figures arenot necessarily to scale, emphasis instead being placed uponillustrating the principles of the invention. Moreover, in the figures,like references numerals designate corresponding parts throughout thedifferent views.

[0020]FIG. 1 depicts the fabrication of a microcapillary networkincorporating aspects of the present invention.

[0021]FIGS. 2A-2D is a schematic representation of the fabrication of amicrocapillary network incorporating aspects of the present invention.

[0022]FIGS. 3A-3D show a host having a three-dimensional microcapillarynetwork residing within the host, which incorporates aspects of thepresent invention.

[0023]FIGS. 4A-4B depict a robotically controlled deposition machine andthe deposition of a fugitive material filament on a substrate.

[0024]FIG. 5 depicts the formation of a host incorporating aspects ofthe present invention that was made by depositing the fugitive materialfilament on the substrate after the uncured host material was applied tothe substrate.

[0025]FIGS. 6A-6C depict the removal of a fugitive material from a hostincorporating aspects of the present invention.

[0026]FIGS. 7A-7D show a device having a two-dimensional microcapillarynetwork incorporating aspects of the present invention residing within ahost fabricated from an epoxy host material.

[0027]FIG. 8 depicts a three-dimensional host incorporating aspects ofthe present invention.

[0028]FIGS. 9A-9C show a host having a three-dimensional microcapillarynetwork of orthogonal passageways, which incorporates aspects of thepresent invention.

[0029]FIG. 9-1 shows an exemplary structure having a three-dimensionalmicrocapillary network of circular and radial passageways, whichincorporates aspects of the present invention.

[0030]FIG. 9-2 shows an exemplary structure having a three-dimensionalmicrocapillary network of non-orthogonal 60° passageways, whichincorporates aspects of the present invention.

[0031]FIG. 10 depicts the formation of a flow altered host using a lightcurable resin and a photomask.

[0032]FIG. 11 depicts a 16-layer three-dimensional structure, whichincorporates aspects of the present invention.

[0033]FIGS. 12A-12D show top and side views of the tower structure of avertically-oriented, square-spiral device, which incorporates aspects ofthe present invention.

[0034]FIG. 13 depicts a co-extruded fugitive material filamentincorporating aspects of the present invention.

[0035]FIGS. 14A-14C depict devices including hosts having one-, two-,and three-dimensional passageways, which incorporate aspects of thepresent invention.

[0036]FIG. 15 depicts mixing patterns in devices including hosts havingone-, two-, and three-dimensional passageways, which incorporate aspectsof the present invention.

[0037]FIG. 16 is a plot of relative mixing intensity versus thestreamwise distance of the passageway in millimeters for representativeone-, two-, and three-dimensional devices.

[0038]FIG. 17 is a plot of relative mixing intensity versus Re forrepresentative one-, two-, and three-dimensional devices.

[0039]FIG. 18 is a plot of rheological data for various fugitivematerials, including a fugitive material that includes a viscositymodifier.

[0040]FIG. 19 is a plot representing the shear stress of a fugitivematerial modified with fumed silica at the 2% and 4% concentration byweight.

DETAILED DESCRIPTION

[0041] Microcapillary devices that include hosts having interconnected,substantially tubular passageways with average diameters from 0.1 to1000 microns are disclosed. Methods of making these hosts, along withpreferable fugitive materials used in the construction of the hosts arealso disclosed. The resultant microfluidic hosts may be used in a vastarray of applications, including biotechnology, self-healing materials,sensors, chemical reactors, and fluidic-based computers.

[0042] Microcapillary Networks

[0043] Microcapillary networks in accord with the present inventioninclude one or more substantially tubular, hollow passageways having aplurality of hollow interconnects. FIGS. 1 and 2A-2D are representationsdepicting the formation of a host 150 having substantially tubularpassageways 105, which may be parallel 110 and perpendicular 120 to theplane of the page, and multiple interconnects 115 between the paralleland perpendicular passageways. The host can be any structure thatcontains the one or more passageways and interconnects. FIG. 2A depictsthe deposition of a fugitive material filament 410, the infiltration ofa host material 140 (FIG. 2B), the solidification of the host materialto form the host 150 (FIG. 2C), and the removal of the fugitive material450 from the host 150.

[0044] As used in the following specification and appended claims,“substantially tubular” means that the majority of the cross-sectionalperiphery of the passageway through the host 150 is curved in shape.Curved can include circular, elliptic, rounded, arched, parabolic andother curved shapes. Examples of substantially tubular passageways areshown, for example, as 105 in FIGS. 3D, 7B, and 9C.

[0045] Unlike in conventional microchannel devices that have square orrectangular microchannel passageways, the passageways in the claimedinvention are not formed by aligning open troughs carved in twosubstrates and then bonding the substrates with the troughs aligned,thus forming a square or rectangular channel. Instead, microcapillarypassageways in accord with the present invention are substantiallytubular in shape.

[0046] The average diameter of the at least one substantially tubularpassageway is preferably from 0.1 micron to 1000 microns and morepreferably from 10 microns to 500 microns. An especially preferredaverage diameter for the passageway is from 50 microns to 250 microns.Hollow interconnects 115 are present in the passageway wherever a firstportion of the passageway contacts a second portion of the passageway,or wherever a first passageway contacts a second passageway. In thismanner, interconnects connect the passageway at a plurality oflocations, thus establishing fluid communication between thepassageways.

[0047] Because the hollow interconnects 115 are formed by contact of oneor more fugitive material filaments having a diameter nearly identicalto that of the passageway, the longest cross-sectional dimension of ahollow interconnect is preferably less than 2.5 times the averagediameter of the one or more passageway that contacts to form theinterconnect. More preferably, the longest cross-sectional dimension ofthe interconnect is less than 2.2 times the average diameter of the oneor more passageway that contacts to form the interconnect. In anespecially preferred embodiment, the longest cross-sectional dimensionof the interconnect is less than twice the average diameter of the oneor more passageway that contacts to form the interconnect. It isunderstood that if an interconnect if formed by more than one contact,such as when three filaments overlap in the z dimension to form twocontacts, the longest cross-sectional dimension of the resultantmulti-contact interconnect (which is actually formed from threefilaments contacting to form two interconnects separated by apassageway) is preferably less than 3.75 times the average diameter ofthe individual filaments.

[0048] Fluids introduced into the microcapillary network through the atleast one passageway in the host can flow through the passageway andthrough the interconnects. Thus, if a host is provided with an inletport and an outlet port, a fluid pumped into the inlet port can flowthrough the one or more passageway and interconnects within the host andout through the outlet port. As used in the specification and appendedclaims, a “fluid” is defined as a substance in the liquid or gaseousstate.

[0049] Preferable microcapillary three-dimensional hosts have at leastone passageway aligned along a first plane in the x and y dimensionsthat extends perpendicular to the first plane in a z dimension andcontinues in a substantially planar fashion in a second x and ydimension plane. In this aspect, the second plane is substantiallyparallel to the first plane. For example, the illustrative host shown inFIG. 3A has a longer x and y than z dimension passageway. Thus, thepassageway 105 in the host is longer in the x and y dimensions than inthe z dimension. In this device, the interconnects 115 are formed in thez dimension when one or more x-y dimension passageway contacts in the zdimension.

[0050] Fabrication

[0051] Microcapillary devices are preferably fabricated with arobotically controlled deposition machine (RCD). An illustration of aRCD 400 is shown in FIG. 4A. FIG. 4B depicts the deposition of afugitive material filament 410 on a substrate 420 by the RCD machine400. Through the computer-controlled, layer-by-layer deposition of thefugitive material filament 410 on a substrate, one-dimensional,two-dimensional, and three-dimensional fugitive material scaffolds 130are formed. Microcapillary devices may then be fabricated when thesescaffolds are removed from the host. As used in the specification andappended claims, “scaffold” is used to describe a two- orthree-dimensional structure made from one or more fugitive materialfilaments. As used in the specification and appended claims, “on” thesubstrate includes when a filament is adjacent to the substrate and whenfilaments are separated by one or more intervening filaments.

[0052] Any substrate 420 may be used that is capable of supporting thedeposited fugitive material scaffold 130. For example, preferablesubstrates may be planar or curved in shape. Preferable substratesinclude those made from glass, plastic, metal, or a combination thereof.

[0053] A deposition head 430 of the RCD machine 400, as depicted inFIGS. 1 and 4B, preferably holds a syringe 440 filled with a fugitivematerial 450. Air pressure may then be used to force the fugitivematerial 450 through the tip of the syringe 440 and out an orifice 460,such as a needle. The fugitive material 450 emerges from the orifice 460as the filament 410 and is deposited by gravity on the substrate 420.

[0054] The average diameter of the filament 410 deposited on thesubstrate 420 may be controlled by the inner diameter of the orifice 460and the pressure applied to the syringe 440. In one preferred aspect,the average diameter of the filament is ±20% that of the orifice, morepreferably ±10%. In an especially preferred aspect, the average diameterof the filament is ±5% that of the extrusion orifice 460.

[0055] In another aspect, the average diameter of the filament 410 isless than that of the orifice 460. A smaller average diameter filamentmay be accomplished by using a fugitive material 450 capable ofself-assembly after extrusion. A more detailed description ofself-assembly may be found in H. Fan, et al., “Rapid Prototyping ofPatterned Functional Nanostructures,” Nature, Vol. 405, pp. 56-60(2000), incorporated by reference in its entirety, except that in theevent of any inconsistent disclosure or definition from the presentapplication, the disclosure or definition herein shall be deemed toprevail.

[0056] Preferably, the average diameter of the extruded filament 410 isfrom 0.1 micron to 1000 microns and more preferably from 10 microns to500 microns. An especially preferred average filament diameter is from50 microns to 250 microns. In a preferred aspect, high precisionelectrical engines move the substrate and/or the filament depositionhead 430 at the desired speed and direction to form the fugitivematerial scaffold. With the planar motion of the substrate (in the x andy directions), the motion of the RCD deposition head (in the zdirection), and the fugitive material flowing from the orifice, it ispossible to build scalable, one-, two-, and three-dimensional scaffolds130 using a layer-by-layer building sequence, for example. In onepreferred aspect, the RCD first deposits the filament onto a moving x-yplatform to yield a two-dimensional scaffold layer. Then, the platformor the RCD head is moved in the z-direction to deposit another x-yscaffold layer. In this manner, scaffolds having 100's of layers in thez dimension may be formed.

[0057] Preferably, the formation of a microcapillary deviceincorporating aspects of the present invention is a three-step processas represented in FIGS. 1 and 2A-2D. A fugitive material 450 may bedeposited from the orifice 460 of the deposition head 430 onto asubstrate 420 to form a scaffold 130 that includes one or more fugitivematerial filaments 410. Representative scaffolds are shown in FIG. 1 andFIG. 2A.

[0058] A host material 140 that infiltrates the scaffold 130, but doesnot substantially infiltrate the filaments 410, may then be deposited onthe scaffold. Substantial infiltration of the fugitive materialfilaments 410 occurs when greater than 20% of the average diameter ofthe filament is penetrated by the host material. Preferably, at least aportion of the scaffold 130 is encapsulated by the host material 140. Inan especially preferred aspect, the entire scaffold is encapsulated bythe host material. Infiltration of the scaffold by the host material isdepicted in FIGS. 1 and 2B. To further stiffen the scaffold 130 andreduce host material infiltration into the filaments, the scaffold maybe cooled prior to host material infiltration, such as to −70° C., tofurther increase the rigidity of the fugitive material.

[0059] The host material 140 may be any material or combination ofmaterials that can fill the interstitial spaces exterior to the scaffoldfilaments 410. Preferred host materials may be deposited as liquids,slurries, or fine powders. More preferred host materials include, butare not limited to, plastics that may be applied in a viscous, liquidstate and cured to form a solid or semi-solid host 150 of a cured hostmaterial.

[0060] Preferable host materials 140 that may be applied as powders orliquids include, but are not limited to, plastics, polyesters,polyamides, polyethers, epoxies, latexes, poly(dimethyl siloxane)(PDMS), their derivatives, and mixtures thereof. At present, anespecially preferred host material that may be deposited as a viscousliquid is epoxy.

[0061] Preferable host materials that may be deposited as slurries orfine powders include ceramics and metals. Preferable ceramics that maybe deposited as host materials include hydroxyapatite, titanium oxide,lead zirconate, titanate, alumina, silica, zirconia, silicon nitride,barium titanate, and silicon carbide, or mixtures thereof. Preferablemetals that may be deposited as host materials include steels,molybdenum, nickel, gold, silver, platinum, titanium-aluminum-vanadiumalloys, tungsten, and aluminum, or mixtures or alloys thereof.

[0062] Curing is the process by which a liquid, paste, powder, or otherformable host material is converted to a solid or semi-solid lessformable host. Examples of a host are depicted in FIG. 1 and FIG. 2C. Inone aspect, curing occurs when monomers or low molecular weight polymersare polymerized to form polymers or higher molecular weight polymers,respectively. In another aspect, curing occurs when a polymer iscrosslinked. In a further aspect, curing involves the conversion of fineor micro-fine flowable particles into a larger, non-flowable mass.

[0063] Curing may be performed by any method known to those of ordinaryskill in the art, including, but not limited to, the addition ofchemical curing agents, exposure to light or other forms of radiation,or heat. If a chemical curing agent is used, it may be added to the hostmaterial 140 before or after the host material is applied to thescaffold 130. At present, an especially preferred curing process relieson the chemical curing of epoxy host materials.

[0064] The host material 140 may be substantially homogeneousthroughout, or optionally modified with particles to change theviscosity or the after curing structural performance of the host 150.However, the portion of the host material containing the fugitivescaffold 130 is not preferably built up by laminating two or morepre-cured layers. In an especially preferred embodiment, the portion ofthe host material 140 encompassing the fugitive material scaffold 130 iscured to form the host 150 in a single step.

[0065] Preferable particles useful for modifying the host material 130include, but are not limited to, plastic and non-plastic particles, suchas ceramics, glasses, semiconductors, and metals. Preferable ceramicparticles include alumina, silica, zirconia, magnesium oxide, zincoxide, tin oxide, titanium oxide, indium oxide, lanthanum oxide, yttriumoxide, calcium oxide, silver oxide, and iron oxide; clays andwhitewares, such as kaolinite, bentonite, and feldspars; carbides, suchas silicon carbide, boron carbide, and tungsten carbide; nitrides suchas silicon nitride, aluminum nitride, and boron nitride; titanates, suchas barium titanate, lead zirconate titanate, and lead zirconatestrontium titanate; ferrites, such as zinc ferrite, manganese ferrite,iron ferrite, cobalt ferrite, nickel ferrite, copper ferrite, magnesiumferrite; manganites, such as manganese manganite and magnesiummanganite; hydroxyapatite; calcium phosphate-based ceramics; diamond;and carbon black; and mixtures thereof.

[0066] Preferable semiconductor particles include silicon; siliconcarbide; III-V semiconducting materials including gallium arsenide,gallium nitride, gallium phosphide, gallium antimide, aluminum antimide,indium arsenide, indium phosphide, and indium antimide; II-VIsemiconducting materials including zinc oxide, cadmium sulfide, cadmiumtelluride, zinc sulfide, cadmium selenide, zinc selenide; and IV-VIsemiconducting materials including lead sulfide and lead telluride; andmixtures thereof.

[0067] Preferable metal particles include iron, tin, zinc, aluminum,beryllium, niobium, copper, tungsten, silver, gold, molybdenum,platinum, cobalt, nickel, manganese, cerium, silicon, titanium,tantalum, and magnesium mixtures and alloys thereof; metal alloys suchas steels and tool steels, stainless steels, plain carbon steels, lowcarbon steels, aluminum-nickel, brass, bronze; and alloys used forbiomedical applications such as cobalt-chromium,cobalt-chromium-molybdenum, cobalt-chromium-tungsten-nickel,cobalt-nickel-chromium-molybdenum-titanium, andtitanium-aluminum-vanadium alloys.

[0068] In addition to particles, microfibers, including, but not limitedto, nylon fibers, glass fibers, carbon fibers, natural fibers, aramid(Kevlar™ and Nomex™) fibers, and mixtures thereof, may also be added tothe host material to alter its structure. Various fibers, supports,brackets, and tubes that allow liquid or gaseous fluids to flow to orfrom the microcapillary device, may also be incorporated into the hostmaterial before or after curing, depending on the application.Electrodes may also be incorporated into the host material before orafter curing, depending on the application.

[0069] As shown in FIG. 5, in another aspect, the uncured host material140 is applied to the substrate before the fugitive material filament410 is deposited on the substrate. As the deposition orifice 460 ismoved through the uncured host material 140, the filament 410 isextruded. As before, the host material is preferably cured to form thehost 150 after the scaffold is complete.

[0070] Independent of the application order of the fugitive and hostmaterials, after curing of the host material 140 to form the host 150,the fugitive material scaffold 130 may be removed. Removal is depictedin FIG. 1 and FIG. 2D. FIGS. 6A-6C are time-lapsed photographs of amicrocapillary device in accord with the present invention as thefugitive material is removed from the host under vacuum. In FIG. 6A theresultant host is shown with the fugitive material scaffolding in place.FIG. 6B depicts the host after a portion of the fugitive material hasbeen removed from the passageways. FIG. 6C depicts the host after thefugitive material has been substantially removed from the passageways.

[0071] While the fugitive material may be removed from the passagewaysin the host by any method, preferably, the fugitive material is heatedand removed under reduced pressure as a liquid. The fugitive materialmay also be removed from the host by flushing the passageways with warmwater or other solvents. When a vacuum is used, the fugitive material isliquefied and a vacuum is applied to at least a first opening in thehost. The fugitive material may then be drawn out of the passageway inthe host as air is drawn into a second opening in the host. Of course,vacuum, solvent, and other methods may be combined to enhance removal ofthe fugitive material 450 from the passageways in the host.

[0072] During construction of the fugitive material scaffold 130,temperature variance may be used to change the mechanical properties ofthe fugitive material 450. In a three-dimensional spanning structure,for example, the deposition of the fugitive material filament may beperformed at reduced temperature to increase the resistance of thefugitive material to flow. In this aspect, cold temperature is used toharden the scaffold in order to minimize the degree of interconnectionthat occurs between the passageways.

[0073] Similarly, elevated temperatures may be used to reduce theviscosity of the fugitive material during removal. By using fugitivematerials demonstrating a temperature dependent viscosity, the degree ofinterconnection between separate portions of the passageway may bealtered. In a preferred aspect, the substrate may be cooled or heated toalter the viscosity of the fugitive material.

[0074] Passageway interconnects 115 can be formed in the host wherever afirst portion of the fugitive material filament contacts a secondportion of a fugitive material filament. Interconnects are formedbecause the host material does not substantially penetrate an area wherefilament contact occurs. The degree of interconnection between a firstand second portion of a passageway can be altered by controlling theamount of filament blending at the contact point, as seen for apartially blended interconnect region 315 in FIG. 3. In one aspect, thismay be accomplished by altering the viscosity of the fugitive materialin relation to temperature. Thus, if little filament blending occurs,the cross-sectional z dimension of the interconnect is preferably alittle less than twice the diameter of the contacting portions of theone or more filaments. Similarly, if nearly complete filament blendingoccurs, preferably from the use of a low viscosity fugitive material,the cross-sectional z dimension of the interconnect will approximate thecross-sectional dimension of the contacting portions of the one or morefilaments.

[0075] If a low viscosity fugitive material is used, a first filamentportion applied atop a second filament portion may fully blend or sinkinto the second filament portion resulting in a large interconnectedarea. Such a “fully blended” interconnect area 715 is visible in thetwo-dimensional microcapillary structure pictured in FIG. 7D. As is seenin the photograph, in this aspect, the locations where the extrudedfilaments overlapped have joined to form the interconnect 115.

[0076] If a higher viscosity fugitive material is used, theinterconnected area can be less because the first filament portion mayblend or sink into the second filament portion a relatively smallamount. In this aspect, the majority of the first filament portionremains above the second filament portion.

[0077] Higher viscosity fugitive materials are preferred forconstructing three-dimensional scaffolds, such as the structure picturedin FIG. 3C. In this structure the passageways running in the x and ydimensions have not fully blended, but retain a significant amount ofthe original filament structure at the interconnect region 315. This isclear when the “fully blended” interconnect region 715 of FIG. 7D iscompared to the partially blended interconnect region 315 of FIG. 3C.

[0078] After removal of the fugitive material 450, a preferredinterconnect is formed if enough overlap occurred between the filamentsto allow a fluid to flow through the interconnect. As previously stated,the degree of interconnection or filament blending may be controlled byaltering the structural integrity or viscosity of the fugitive material.

[0079] Benefits of the present fabrication method in relation toconventional methods may include, but are not limited to: the use of aRCD as opposed to lithography; a lithography master is not required; themicrocapillary device does not have to be assembled from multiplelayers; the microcapillaries may be constructed within any material thatcan serve as a host material, including structural polymers such asepoxy; the microcapillaries can be made in a single step; manufacturingtime may be less than 24 hours, depending on the curing time of the hostmaterial.

[0080] Two-Dimensional Microcapillary Networks

[0081] Preferably, two-dimensional microcapillary networks are formed bydepositing a lower viscosity fugitive material on a single plane. Theheight of the RCD deposition head may remain constant during thedeposition. FIG. 7A depicts a two-dimensional microcapillary networkresiding within an epoxy host material. Interconnects may be formed atabout 26.5° angles and are separated by about 0.895 mm.

[0082]FIG. 7B shows a two-dimensional network passageway having anaverage cross-sectional diameter of about 135 μm. The depictedpassageway has an average width of about 180 μm and an average height ofabout 90 μm. A syringe equipped with a 100 μm orifice needle was used todeposit the fugitive material filament that resulted in the formation ofthis passageway. As can be seen from the figure, although some“flattening” occurred where the fugitive material filament contacted thesubstrate 420, the passageway lacks 90° angles and is substantiallytubular. Unlike in conventional microchannel devices, and as can be seenin FIG. 7B, the passageways are not square or rectangular in shape. FIG.7C shows a top view of the hollow interconnect region of atwo-dimensional microcapillary network as a liquid 710 is introducedfrom the left side of the device, thus forcing air 720 to the right.

[0083] Three-Dimensional Microcapillary Networks

[0084] In a preferred aspect, three-dimensional networks are made in asimilar fashion as two-dimensional networks; however, a more viscous(structurally stronger) fugitive material is used to reduce the amountof interconnection that occurs when fugitive material filaments contactand bridge underlying filaments. If the structural integrity of thefugitive material is too low, the filaments applied atop other filamentscould sink into the lower filaments and loose the three-dimensionalstructure of the scaffold.

[0085]FIG. 3A depicts a drawing of a three-dimensional microcapillarynetwork. As can be seen from the lower right depiction of a z-axiscross-section, the passageway has multiple interconnects formed whereupper and lower passageways contact. FIGS. 3B and 8 are photographs ofrepresentative hosts having three-dimensional passageways. FIG. 3C is aphotograph of the top of the host showing a cured epoxy host material140 residing in the interstitial areas of the passageways 105. FIG. 3Dis a photograph of a cross-section of the host depicting thesubstantially tubular nature of the passageways 105. Unlike in thetwo-dimensional host passageway shown in FIG. 7B, very little“flattening” of the fugitive material is observed due to the increasedviscosity of the fugitive material used to form the device of FIGS.3A-3D and 8.

[0086]FIGS. 9A-9C depict a complex three-dimensional fugitive materialscaffold incorporating features of the present invention. FIG. 9A is aphotograph of a top view of a 16-layer microcapillary scaffold. An epoxyhost material can then be infiltrated into the scaffold and cured togive the host shown in FIG. 9B. The fugitive material may then beremoved by heating under light vacuum to give a microcapillary networkwithin the host. FIG. 9C depicts a scanning electron microscope image ofa cross section of the host after the fugitive material is removed. Thesubstantially tubular nature of the passageways 105 is evident.

[0087] Due to the plethora of fugitive material scaffolds that may bedesigned using the claimed methods, an almost infinite collection ofmicrocapillary structures are possible. For example, in FIG. 9-1 anexemplary three-dimensional structure 910 having alternating circularpassageways that form interconnects with straight radial arms are shown.Another exemplary structure, similar to the device of FIG. 9A, isdepicted in FIG. 9-2. However, unlike the FIG. 9A device that has anorthogonal (90°) orientation between successive passageways along thez-axis, the FIG. 9-2 structure 920 has a 60° orientation betweensuccessive passageways.

[0088] In another aspect, a microcapillary device may be formed in whicha portion of one or more passageways and/or a portion of theinterconnects in the host are sealed by a cured resin, as depicted inFIG. 10. By introducing a curable resin 1005 into the host, andselectively curing a portion of the resin, a host having an altered flowpattern may be formed. In a preferred aspect, the host is at leastpartially filled with a photocurable resin 1005. In an especiallypreferred aspect, the host is filled with a photocurable epoxy resin,such as Ultraviolet cure adhesive Model 61, Norland Products, Cranbury,N.J.

[0089] A portion of the curable resin is then selectively cured in thepassageways 105 and/or interconnects 115 of the host. In an especiallypreferred embodiment, selective curing is performed by placing apatterned mask or photomask 1010 on the host 150 and using light of anappropriate wavelength to cure the portion of the curable resin 1005below open areas 1015 of the mask 1010. This process is represented inFIG. 10 and can result in selective sealing of passageways and/orinterconnects in the host, allowing for additional control over fluidflow within the host. Preferably, the previously cured host material 105is at least partially transparent to the radiation wavelength used tocure the sealing resin. The uncured resin 1005 may then be removed fromthe internal portions of the device that were shielded from the light toyield a host incorporating a flow altered microcapillary device.

[0090] In one aspect, this flow alteration method is used to produce ahost having vertically-oriented, square-spiral, internal mixing towers.In another aspect, a host having vertically-oriented, triangular-spiral,internal mixing towers is formed. In another aspect, hosts havingtwisted-pipe internal structures may also be formed.

[0091] An example of a microcapillary structure 1100 incorporating avertically-oriented, square-spiral mixing tower is shown in FIG. 11.FIG. 12A is a top-down view of a single square-spiral tower formed bythe unsealed passageways and interconnects within the host. FIG. 12C isa side-view of the architecture showing the interconnect regions 115.FIGS. 12B and 12D show top and side views of possible fluid flowpatterns within a square-spiral architecture device. The lighter areasto the exterior sides of the darker central area represent passagewayssealed by the curable resin. In a preferred aspect, the deviceincorporating a host of this design is believed to have improved fluidmixing characteristics provided by chaotic advection.

[0092] While not shown in the figures, a portion of the passagewaysand/or interconnects could also be sealed in a host having the exemplarystructure of FIG. 9-2 to yield a triangular-spiral architecture withinthe host. In relation to the square-spiral architecture of the FIG. 12device, the passageway turns through which a fluid would flow in atriangular-spiral internally structured host would be sharper. A devicecontaining a host having triangular-spiral internal architecture wouldlikely have enhanced mixing efficiency in relation to the square-spiraldevice.

[0093] Fugitive Materials

[0094] Fugitive materials 450 are preferably capable of forming thedesired scaffold 130 and being substantially removed from the host 150.As used in the specification and appended claims, substantially removedmeans that at least 80%, more preferably at least 90%, and in anespecially preferred aspect, at least 97% of the total weight offugitive material used to form the scaffold is removed from the host.

[0095] Scaffold fabrication can exploit three desirable properties ofthe fugitive material: a well-controlled viscoelastic response, theability to maintain shape during infiltration and curing of the hostmaterial, and the ability to undergo a solid-to-liquid phase transitionat modest temperature, thus facilitating its removal to form the finalmicrocapillary structure in the resultant host.

[0096] Viscoelastic response refers to the combination of theshear-thinning behavior and the viscosity of the fugitive material.Shear-thinning represents the decrease in viscosity of a fluid undershear forces. Thus, good shear-thinning behavior allows the fugitivematerial to flow from a small orifice during deposition and rapidly“set” to facilitate shape retention of the deposited features.

[0097] Preferably, once deposited, the fugitive material has a viscosityhigh enough to provide the necessary structural support to form andpreserve a three-dimensional scaffold, even as the filament spans gapsin the underlying filament layers. Thus, fugitive materials preferredfor forming three-dimensional scaffolds are capable of maintaining athree-dimensional shape, without collapse, under deposition conditions.

[0098] Fugitive materials having a temperature dependent viscosity areespecially preferred. Preferable fugitive materials having temperaturedependent viscosity can maintain the complex structure of the scaffoldwhen cold, and liquefy when hot. In one aspect, a preferable fugitivematerial can extrude from the deposition orifice and have sufficientinternal strength to span underlying fugitive material scaffolding whilemaintaining its shape.

[0099] In another preferred aspect, the fugitive material is at leastpartially transparent to the irradiation wavelength used to cure thehost material, if the host material is radiation cured. Thus, ifultraviolet light is used to cure the host material, a preferablefugitive material would be at least partially transparent to ultravioletlight.

[0100] Preferred fugitive materials are organic materials with orwithout inorganic constituents. More preferred fugitive materialsinclude at least 80% nonvolatile components by weight. At present,especially preferred fugitive materials include a majority of organicconstituents by weight. Examples of fugitive materials that areespecially preferred at present include Prussian blue paste (Loctite™,Rocky Hill, Conn.), petroleum jelly (Vaseline™, Unilever, EnglewoodCliffs, N.J.), various lubricants (CIP™, McGlaughlin Oil Co., Columbus,Ohio, for example), and lubricants combined with viscosity modifiers,such as CIP™ Lube containing fumed silica particles. Prussian blue pastecan contain 80-85% paraffinic hydrocarbon, 5-10% ferric ferrocyanide,and 1-15% mineral oil. CIP™ lubricant can contain 50-75% white mineraloil, 1-10% aluminum sterate, and 5-20% other constituents.

[0101] By mixing various organic materials with inorganic constituents,the viscosity of the fugitive material may be modified. Thus, to achievethe desired viscosity performance of the fugitive material, one or moreviscosity modifiers may be combined with one or more base materials,such as Prussian blue paste, petroleum jelly, or lubricants, to give thedesired characteristics to the fugitive material.

[0102] Preferable viscosity modifiers that may be added to a basematerial to form fugitive materials include, but are not limited to,porous colloid particles, such as fumed silica (M-5P fumed silicaparticles, Cab-O-Sil™, Cabot division, Alpharetta, Ga.), calcium complexrods, lithium hydroxystearate fibers, liquid crystals, viscoelasticmicelles, low molecular weight polymers (oligomers), glass and polymerbeads, polymer and ceramic microcapsules, polymer, ceramic, and metalshort fibers. Any one or more of these viscosity modifiers may becombined with an organic containing base, CIP™ Lube for example, to givea fugitive material in accord with the present invention.

[0103] A more detailed discussion of the use of calcium complex rods andlithium hydroxystearate fibers to modify an organic containing basecomposition may be found in Mas, R., and Magnin, A., “Rheology ofcolloidal suspensions: case of lubricating grease,” Journal of Rheology,Vol. 38, No. 4, 1994, pp. 889-908, incorporated by reference in itsentirety, except that in the event of any inconsistent disclosure ordefinition from the present application, the disclosure or definitionherein shall prevail. A more detailed description of liquid crystals andviscoelastic micelles and their use as viscosity modifiers may be foundin Bautista, F., de Santos, J. M., Puig, J. E., and Manero, O.,“Understanding thixotropic and antithixotropic behavior of viscoelasticmicellar solutions and liquid crystalline dispersions. I. The model.”Journal of Non-Newtonian Fluid Mechanics, Vol. 80, 1999, pp. 93-113,incorporated by reference in its entirety, except that in the event ofany inconsistent disclosure or definition from the present application,the disclosure or definition herein shall prevail.

[0104] In one preferred aspect, fugitive materials contain less than 10%by weight and more preferably less than 5% by weight of one or acombination of viscosity modifiers. In an especially preferredembodiment, the fugitive material contains less than 2.5% by weight ofone or a combination of viscosity modifiers.

[0105] When porous colloidal particles are used as viscosity modifiers,the particles preferably have average diameters from 10 to 30 nm. Theaddition of porous colloidal particles may be used to modify thestiffness of organic and organic/inorganic compositions to improve theirperformance as fugitive materials. An example of the improvementobtained in shear stress when a viscosity modifier is combined with anorganic containing base is seen in FIG. 18. As seen in the graph, shearstress not only increases, but becomes more uniform as a function oftime when CIP™ Lube is modified with about 2% by weight of fumed silicaporous colloidal particles.

[0106] Fugitive materials may also be co-extruded. If an orifice 460with more than one passageway is used to extrude the scaffoldingfilament, the filament may include more than one fugitive material, or afugitive material in combination with a non-fugitive material. Forexample in FIG. 13, a fugitive material filament is shown having aninner material 1310 of Prussian blue paste and an outer material 1320 ofVaseline™ petroleum jelly. In this way, microcapillary devices may beformed where the viscosities of multiple fugitive materials are used tocontrol interconnection.

[0107] In addition to providing additional viscosity control,co-extrusion of a non-fugitive material with a fugitive material, canresult in a host having microcapillary passageways that are lined withor have an inner core of a non-fugitive material. For example, if anon-fugitive material, such as a colloidal ink or a pseudoplastic slurrycontaining ceramic or metal particles, is co-extruded external to thefugitive material, microcapillary passageways that are lined with metalor plastic particles can be formed in the host material when the ink orslurry solidifies. Any desired particles that are compatible withmicrocapillary device construction can be included in the non-fugitivematerial. Similarly, if the non-fugitive inks or slurries areco-extruded internal to the fugitive material, their solidified networkcan remain in the host when the fugitive material is removed.

[0108] A more complete discussion of non-fugitive colloidal inks andtheir uses may be found in Smay, J. E., et al., Colloidal Inks forDirected Assembly of three-dimensional Periodic Structures, Langmuir,18, 5429-37 (2002), incorporated by reference in its entirety, exceptthat in the event of any inconsistent disclosure or definition from thepresent application, the disclosure or definition herein shall prevail.A more complete discussion of non-fugitive pseudoplastic slurries andtheir uses may be found in U.S. Pat. No. 6,027,326, incorporated byreference in its entirety, except that in the event of any inconsistentdisclosure or definition from the present application, the disclosure ordefinition herein shall be deemed to prevail.

[0109] Representative Applications

[0110] As previously stated, microchannel-type devices, such as theclaimed microcapillary devices and hosts, have many uses, includingbiotechnology, self-healing materials, sensors, chemical reactors(lab-on-a-chip), and fluidic-based computers. Liquids alone or liquidscontaining solids, such as biomolecules, DNA, RNA, proteins, organicmaterials, inorganic materials, and combinations thereof may be mixed inthe claimed microcapillary devices. A more detailed description of theuse of microchannel-type devices as microfluidic devices in biomedicaland in biotechnology applications may be found in Burns, M. A., et al.,An integrated nanoliter DNA analysis device. Science 282, 484-487(1998); Chou, H.-P., et al., A microfabricated device for sizing andsorting DNA molecules. Proc. Nat. Acad, Sci. 96, 11-13 (1999);Strömberg, A., et al., Microfluidic device for combinatorial fusion ofliposomes and cells. Anal. Chem. 73, 126-130 (2001); and Choi J.-W., etal., An active microfluidic mixer for mixing of microparticles andliquids. SPIE Proceedings 4177, The International Society for OpticalEngineering, 154-161 (2000).

[0111] The claimed microfluidic devices can also form the capillarynetwork within a polymer or composite material that allows for automatedrepair. In this application, a microcirculatory system may beincorporated into the material to replenish the supply of healing agentand catalyst to the material.

[0112] For example, if an airplane wing contains microfluidiccapillaries (passageways and interconnects) that contain a liquidmaterial that cures on exposure to air, a crack in the wing can beautomatically repaired when the liquid material oozes from the channelsand fills the crack. Such self-healing (autonomic) materials may be usedin airplane components, space vehicles, satellites, surface andsubsurface water craft, buildings, and bridges, for example. Inspacecraft, for example, the liquid material could cure on exposure toradiation. In watercraft, for example, the liquid material could cure onexposure to water. A more detailed discussion of self-healing materialsmay be found in White, S. R., et al., Autonomic healing of polymercomposites. Nature 409, 794-97 (2001).

[0113] By using multiple deposition orifices, the claimed microfluidichosts can be formed within coatings on a large scale. For example, alarge metal or composite plate may be coated with a microfluidic device.In one aspect, a RCD having a plurality of deposition heads may be usedto form a scaffold from a fugitive material on the steel plate.Depending on the size of the plate, 100's of deposition orifices may beutilized. The plate and the scaffold may then be covered by a coating,such as epoxy containing paint. The fugitive material may then beremoved to leave a periodic structure in the coating. The periodicstructure may be tuned to adsorb radiation at one or more wavelengths.

[0114] Microfluidic hosts may also be incorporated into sensor devicesor devices used as miniature chemical reactors, as discussed inChabinyc, M. L., et al., An integrated fluorescence detection system inpoly(dimethylsiloxane) for microfluidic applications. Anal. Chem. 73,4491-4498 (2001); Losey, M. W., et al., Microfabricated multiphasepacked-bed reactors: characterization of mass transfer and reactions.Ind. Eng. Chem. Res. 40, 2555-2562 (2001); and Jeon, N. L., et al.,Generation of solution and surface gradients using microfluidic systems.Langmuir 16, 8311-8316 (2000), for example. By selectively sealingportions of the passageway and interconnects within the host, variousfluids and reagents may be directed to specific locations within thehost. By equipping the device with electrodes prior to or after curingof the host material, an electric potential may be used to directcharged reagents. Furthermore, microfluidic devices have also been usedas the basis for computers as described in Moore, S. K., Microfluidicsfor complex computation. IEEE Spectrum 38, 28-29, (2001).

[0115] The preceding description is not intended to limit the scope ofthe invention to the preferred embodiments described, but rather toenable a person of ordinary skill in the art of microchannel-type devicefabrication to make and use the invention. Similarly, the examples beloware not to be construed as limiting the scope of the appended claims ortheir equivalents, and are provided solely for illustration. It is to beunderstood that numerous variations can be made to the procedures below,which lie within the scope of the appended claims and their equivalents.

EXAMPLES Example 1 Fabrication of One- and Two-DimensionalMicrocapillary Networks

[0116] Straight passageway (one-dimensional) and square-wave channel(two-dimensional) microfluidic devices were fabricated by roboticallydepositing an optically clear lubricant (CIP™ Lube, McGlaughlin OilCompany) onto a glass cover slide. The CIP™ Lube was housed in a syringe(barrel diameter=4.6 mm, EFD Inc.) and deposited through a cylindricalnozzle (diameter, D=150 μm) at a constant deposition speed (v) of 6mm/s.

[0117] The one-dimensional and two-dimensional passageway hostsconsisted of a single layer pattern of a 45° Y-junction connected to a17-mm long straight channel or a 15 mm long square-wave channel withseven C-turns (size˜0.5 mm), respectively. The total build time wasapproximately 60 seconds for each patterned feature.

[0118] Three rubber tubes were then placed at the two inlet and oneoutlet nodes associated with each scaffold. The tubes were filled withthe fugitive material to ensure their connections to the depositedscaffold. The scaffolds were encapsulated with the epoxy resin (2.5:1epoxide to aliphatic amine curing agent) and cured at 22° C. for 24 hand 60° C. for 2 h to form a host. At 60° C. the fugitive material wasremoved from the host under a light vacuum.

Example 2 Fabrication of a Three-Dimensional Microcapillary Scaffold

[0119] A three-dimensional, fugitive material scaffold in accordancewith the present invention was made by the following procedure. Thethree-dimensional scaffold was fabricated using a robotic depositionapparatus (Model JL2000, Robocasting Enterprises, Inc., Albuquerque,N.Mex.). This direct-write technique employed an ink delivery systemmounted on a z-axis motion control stage for agile printing onto amoving x-y stage. Three-axis motion was independently controlled by acustom-designed, computer-aided direct-write program (RoboCAD 2.0) thatallowed for the construction of three-dimensional scaffolds in alayer-wise deposition scheme.

[0120] An organic ink (Prussian blue paste, Loctite®, Rocky Hill, Conn.)was housed in a syringe (barrel diameter=4.6 mm, EFD Inc., EastProvidence, R.I.). The ink was deposited through a cylindrical nozzle(diameter, D=200 μm) at a volumetric flow rate (=0.25πD²v) required tomaintain a constant deposition speed (v) of 15 mm/s.

[0121] A two-dimensional pattern of cylindrical rods was created with aninter-rod separation distance of 1.25 mm. After a given layer wasgenerated, the stage was incremented in the z-direction (z=170 μm=0.85D)and another layer was deposited with a 90° rotation and 0.5 mm planarshift from the underlying layer. This process was repeated until thedesired three-dimensional (16-layer) scaffold was created. The totalbuild time for a given three-dimensional structure was approximately 180seconds.

Example 3 Fabrication of a Three-Dimensional Microcapillary Network

[0122] The fugitive material scaffold from Example 2 was placed in aPetri dish and cooled on a dry ice and acetone bath (−70° C.). Thescaffold was then infiltrated with a liquid resin consisting of 2.5:1epoxide (EPON 828, Shell Chemicals) to aliphatic amine curing agent(EPI-CURE 3274, Shell Chemicals). The resin was cured at 22° C. forabout 24 h and then at 60° C. for about 2 h to form the host. At 60° C.,the scaffold liquefied and was removed from the host under a lightvacuum yielding the desired microcapillary network of interconnected,substantially tubular passageways.

Example 4 Fabrication of a Three-Dimensional Microcapillary NetworkHaving a Vertically-Oriented, Square-Spiral Internal Architecture

[0123] A photosensitive monomer (Model 61, Norland Products) wasinfiltrated into the microcapillary network of Example 3. This structurewas then masked and selected channels were photopolymerized by UV curingfor about 60 s. The photomask was generated by printing the desiredpattern on a transparency using a high-resolution printer (5,080 dpi). Afiltered UV light source (U-MNUA, type BP360-370) was mounted on anOlympus Epi-fluorescent microscope (BX-60). Uncured monomer was removedunder a light vacuum.

Example 5 Fluid Mixing Experiments in One-, Two-, and Three-DimensionalDevices

[0124] Mixing experiments were carried out in the one-dimensional,two-dimensional, and three-dimensional microfluidic devices describedabove by simultaneously flowing two aqueous fluids containing red orgreen fluorescent dyes (0.60 mg/ml of H₂O, Bright Dyes). Mixingefficiency was characterized by measuring the yellow color intensityproduced upon fluid mixing using a fluorescence light microscope (ZeissAxiovert 100, Carl Zeiss). The images were captured through a tripleexcitation filter (360/480/560) attached to a color CCD cameracontrolled with MCID software (MCID v.6, Imaging Research). The fluidswere housed inside 10 cc syringes mounted side-by-side on a syringe pump(PHD 2000, Harvard apparatus).

[0125] In the three-dimensional device, the fluids were attached toMicrofil® syringe tips (Microfil®, World Precision Instruments)previously inserted in the two inlet pore channels (diameter˜230 μm) andsealed. For the one-dimensional and two-dimensional devices, thesyringes were directly connected to the passageways via the tubinginserted prior to host material infiltration. For each mixingexperiment, the device was placed on the specimen stage of thefluorescent microscope and the two inputs were connected to the syringescontaining the red and green fluorescent fluids, while the output waslinked to a waste reservoir. The syringe pump was set to the desiredflow rate (0.1-45 ml/h) and the mixing behavior was then observed. Allfluorescent images were captured under steady-state conditions (>180 s).Image processing was performed with Photoshop (Photoshop v.6, Adobe) forcolor filtering and MCID (MCID v.6, Image research) for pixel intensitymeasurements.

Example 6 Fluid Mixing in a Three-Dimensional Device HavingVertically-Oriented, Square-Spiral Mixing Towers was Compared to that ofOne-Dimensional and Two-Dimensional Devices

[0126] The mixing efficiency of the three-dimensional square-spiraltowers (shown in FIG. 14C) was characterized by monitoring the mixing oftwo fluid streams (red and green) using fluorescent microscopy as afunction of varying Re˜0.15-70. Re is the Reynolds number (Re=UI/v)where U is the average flow speed, I is the characteristiccross-sectional dimension of the channel, and v is the kinematicviscosity of the fluid. The value is a dimensionless ratio of inertialto viscous forces. In general, higher Re values correspond to fasterfluid flow rates through the device. For comparative purposes, fluidmixing was also characterized in two alternate microfluidic devices: astraight (one-dimensional) passageway (FIG. 14A) and a square-wave(two-dimensional) passageway (FIG. 14B). After the two fluid streamscome into contact, the red and green fluorescent dyes begin to diffuseresulting in the formation of a yellow (mixed) fluid layer. Mixing isbelieved to occur solely by molecular diffusion in the one-dimensionaldevice, which serves as a benchmark for evaluating mixing efficiency ofboth the two- and three-dimensional devices.

[0127] Optical images of the one-, two-, and three-dimensionalmicrofluidic devices at representative low (Re<1), intermediate(1<Re<10), and high Re (>10), are shown in FIG. 15. A thin zone of mixed(yellow) fluid was observed at the center of the one-dimensionalchannel, whose width decreased with increasing Re due to a correspondingdecrease in residence time at higher flow rates.

[0128] At low and intermediate Re, a central zone of mixing appeared inthe two-dimensional device that followed the contour of thesquare-channel array. At high Re, the mixing zone appears to undulatefrom the channel walls as fluid traverses through the array, at timesfilling the entire channel cross-section. The appearance of multiplemixing zones across the channel cross-section is indicative oftransverse flow that twists and folds the fluid interface.

[0129] In the three-dimensional device, this behavior was apparent evenat low Re as the fluid stream is constantly reoriented by passing fromsegment to segment (90° turns) within the square-spiral towers. Atintermediate Re the filtered image reveals increasing complexity in theflow domain with the appearance of multiple mixing zones and striationsacross the channel cross-section. At large Re the mixing processoccurred rapidly, and a fully mixed stream was achieved shortly afterentering the second spiral tower.

[0130] To quantify the degree of mixing, the average yellow intensity

I

was measured across the channel and compared to the intensity obtainedwhen the two fluids were completely mixed

I_(mix)

prior to their introduction to the channel. The relative intensity{overscore (I)}═

I

/

I_(mix)

, where

denotes the average taken over all pixels imaged in a given microchannelsegment, ranges from 0 (unmixed) to 1 (fully mixed). {overscore (I)} isplotted as a function of streamwise distance in FIG. 16 for eachmicrofluidic device at Re=30.6. The figure shows that thethree-dimensional (3-D) device had superior mixing performance to itsone- (1-D) and two-dimensional (2-D) counterparts.

[0131] Diffusive mixing was the dominant mechanism observed for theone-dimensional straight passageway at all Re values considered as wellas the two-dimensional square-wave passageway in the Stokes flow regime(Re<1). The growth of the mixed zone normal to the flow direction (i.e.,the radial dispersion) scaled as {square root}{square root over (Dt)}(where D=1.67×10⁻⁶ cm²/s), or as x^(1/2) for steady flow conditionswhere x is the streamwise distance. A more detailed discussion ofstreamwise distance can be found in Jones, S. W., Interaction of chaoticadvection and diffusion. Chaos Applied to Fluid Mixing, Aref, H. and ElNaschie, M. S., eds., 185-196 (1995). Mixing was found to markedlyimprove relative to diffusion alone for both the two-dimensionalsquare-wave passageway at high Re and in the three-dimensional squarespiral towers over the studied Re values. The oscillatory nature of the{overscore (I)} data is believed to reflect the folding and twisting ofthe fluid interface as it is advected along a given channel within suchstructures.

[0132] Viewing the two-dimensional device from above, it appears thatthe mixed interface undulates across the channel when the streamlinesperiodically act to spin the interface into a planar profile. In theStokes flow regime, these oscillations are greatly exaggerated for thethree-dimensional device owing to the higher degree of twisting andfolding of the mixing interface as the fluid stream negotiates eachapproximately 90° turn within the tower. At higher Re, theseoscillations are damped and complete mixing occurs rather quickly,within about 45 msec. (or a streamwise distance of 6 mm) at Re˜30.

[0133] The relative intensity {overscore (I)} is plotted as a functionof Re in FIG. 17 for each microfluidic device. These data are reportedat a constant streamwise distance of 14 mm, which corresponds to theoutlet of the second tower of the three-dimensional device. The degreeof mixing arising solely from diffusion under pure laminar flowconditions (one-dimensional case) decreased rapidly with increasing Re,as the residence time was reduced within the passageway. Mixing in thetwo-dimensional device was diffusion dominated at low Re beforeincreasing linearly above Re˜10. Complete mixing was not observed forthe two-dimensional device until Re˜70. The mixing performance for thethree-dimensional microfluidic device was characterized by two distinctregimes. At low Re, diffusive mixing dominated leading to a decrease inrelative intensity as Re increased from 0.15 to ˜1.0. It should be notedthat this tower geometry led to an approximate two-fold enhancement ofmixing at Re=0.15 relative to either the one-dimensional ortwo-dimensional case under the same conditions. At Re 1, a transition inbehavior was observed and mixing was thereafter increasingly dominatedby what was believed to be chaotic advection. Above this transition,mixing was greatly accelerated and nearly complete mixing was achievedat Re>15.

[0134] While complete mixing remained diffusion-limited (i.e., occurringover the diffusive length scale l_(D)≈(D_(mol)t)^(1/2)), chaoticadvection was thought to have stretched and folded the fluid interfaceinto long tendrils with the flow domain consisting of interwovenstriations of the two fluids. The separation distance between thestriations for a steady, chaotically advecting flow will decreaseexponentially with streamwise time distance along the tower (cf.l_(sep)≈2A/l₀exp(λt) for the time-dependent case, where A is the area ofthe flow domain, I₀ is the initial perimeter of the mixing two-fluidinterface, and λ is the Lyapunov exponent of the advecting flow). Ahomogenous mixture may be obtained when the striation separations andthe diffusion length are comparable. The relative intensity approachedunity (fully mixed) at an exponential rate for the three-dimensionalsquare-spiral towers above this transition (see FIG. 17), since the timescale for homogenization grows with natural log of the Peclet number(i.e., t_(hom)∝ln(Pe)). Such observations are taken as strong evidencefor the dominance of chaotic advection in this regime.

Example 7 Preparation of a Fugitive Material Using Porous ColloidalParticles

[0135] For fugitive materials, the yield stress (τ_(y)) was identifiedas an important parameter for the deposition of a three-dimensionalscaffold having spanning filaments. This parameter corresponds to theshear stress at low shear rate. To increase yield stress of a lubricant,M-5P fumed silica particles (Cab-O-Sil® Cabot division) were added tothe CIP Lube® lubricant. A yield stress increase of approximately oneorder of magnitude was measured for a mixture of lubricant with 2% byweight silica particles. In addition, no intermediate plateau wasobserved for the shear stress value during the monotonic increase withincreasing shear rate. These results demonstrate that even at low volumefractions, the addition of nanoscale reinforcements can significantlyimpact the rheological properties of organic materials.

[0136] Also, oscillatory experiments were performed at room temperatureon CIP Lube® lubricant with 2% and 4% (wt) fumed silica particles. Themeasured shear storage modulus (G) as a function of shear stress ispresented in FIG. 19. At 2% (wt) particle concentration, the shearstorage modulus shows a low stress plateau value of about 3 kPa.Softening begins to occur above 20 Pa until dropping precipitously above100 Pa shear stress. This drastic reduction in storage moduluscorresponds to the yield stress (τ_(y)) of the material and the end ofthe elastic regime. At 4% (wt) particle concentration, the shear storagemodulus plateau is much higher (˜1 MPa) and extends to a much highershear stress range (τ˜100-1,000 Pa). Based on these results, a twoorders of magnitude increase in storage modulus was obtained by doublingthe volume fraction of added particles.

[0137] As any person of ordinary skill in the art of microchannel-typedevice fabrication will recognize from the provided description,figures, and examples, that modifications and changes can be made to thepreferred embodiments of the invention without departing from the scopeof the invention defined by the following claims and their equivalents.

What is claimed is:
 1. A device comprising: a host having definedtherein at least one substantially tubular, hollow passageway throughsaid host, wherein said passageway has an average diameter from 0.1micron to 1000 microns; and a plurality of hollow interconnects, whereinsaid interconnects are formed when a first portion of said passagewaycontacts a second portion of said passageway or a second passageway, andwherein said interconnects connect the first portion of said passagewayto at least the second portion of said passageway or to the secondpassageway thereby establishing fluid communication.
 2. The device ofclaim 1, wherein the longest cross-sectional dimension of saidinterconnect between the first and the second portion of said passagewayis less than 2.5 times the average diameter of said passageway.
 3. Thedevice of claim 1, wherein the longest cross-sectional dimension of saidinterconnect between the first portion of said passageway and the secondpassageway is less than 2.5 times the average diameter of saidpassageway.
 4. The device of claim 1, wherein said passageway has anaverage diameter from 10 microns to 500 microns.
 5. The device of claim1, wherein said passageway has an average diameter from 50 microns to250 microns.
 6. The device of claim 1, wherein said host comprises aceramic.
 7. The device of claim 1, wherein said host comprises a metal.8. The device of claim 1, wherein said host is selected from the groupconsisting of plastics, polyesters, polyamides, polyethers, epoxies,latexes, poly(dimethyl siloxane), their derivatives, and mixturesthereof.
 9. The device of claim 1, wherein said host is substantiallyhomogeneous throughout.
 10. The device of claim 1, wherein said hostcomprises a plastic.
 11. The device of claim 10, wherein said plastic isan epoxy.
 12. The device of claim 10, wherein said plastic comprisesnon-plastic particles.
 13. The device of claim 12, wherein saidparticles comprise a metal.
 14. The device of claim 12, wherein saidparticles comprise a ceramic or a glass.
 15. The device of claim 12,wherein said particles comprise a semiconductor.
 16. The device of claim1, wherein said host comprises microfibers.
 17. The device of claim 16,wherein said fibers are selected from the group consisting of nylonfibers, glass fibers, carbon fibers, natural fibers, aramid fibers, andmixtures thereof.
 18. The device of claim 1, further comprising an inletport and an outlet port, wherein said ports are in fluid communicationwith the at least one passageway, such that when a fluid is introducedto the inlet port, the fluid may flow through the at least onepassageway and the interconnects and exit the host through the outletport.
 19. The device of claim 18, wherein said fluid is selected fromthe group consisting of liquids, gases, and combinations thereof. 20.The device of claim 1, wherein said passageway comprises a first portionextending along a first plane in the x and y dimensions, a secondportion extending perpendicular to the first plane in a z dimension, anda third portion extending in a substantially planar fashion in a secondx and y dimension plane that is substantially parallel to the firstplane.
 21. The device of claim 20, wherein said passageway is longer insaid planar dimension than in said perpendicular dimension.
 22. Thedevice of claim 20, wherein said interconnects are formed in saidperpendicular dimension.
 23. The device of claim 1, wherein saidinterconnects only form in a dimension perpendicular to said passageway.24. The device of claim 1, wherein said passageway has a cross-sectionalperiphery comprising at most one flattened portion, and the remainingnon-flattened portion of the periphery is curved in shape.
 25. Thedevice of claim 1, wherein said passageway is formed by removing afugitive material from an interior of said host.
 26. The device of claim1, wherein said passageway and said interconnects are formed by removinga fugitive material from an interior of said host.
 27. The device ofclaim 1, wherein said passageway is not formed by joining two or moreopen troughs.
 28. The device of claim 1, wherein a portion of saidpassageway, a portion of said interconnects, or a portion of saidpassageway and a portion of said interconnects is sealed with a curedresin.
 29. The device of claim 28, wherein said host comprises a hollow,vertically-oriented, square-spiral mixing tower.
 30. The device of claim1, wherein at least a portion of said passageway is lined with anon-fugitive material.
 31. The device of claim 30, wherein saidnon-fugitive material comprises a solidified colloidal ink.
 32. Thedevice of claim 30, wherein said non-fugitive material comprises asolidified pseudoplastic slurry.
 33. The device of claim 1, wherein atleast a portion of said passageway is partially filled with a solidifiedcolloidal ink.
 34. The device of claim 1, wherein at least a portion ofsaid passageway is filled with a solidified pseudoplastic slurry. 35.The device of claim 1, where the host is a coating on the surface of thedevice.
 36. The device of claim 1, wherein the device is a biomedicalmicrofluidic device.
 37. The device of claim 1, wherein said device isan aircraft structure.
 38. The device of claim 1, wherein said device isa space vehicle or a satellite.
 39. The device of claim 1, wherein saiddevice is a surface or a subsurface water craft.
 40. The device of claim1, wherein said device is a bridge or a building.
 41. A method ofclosing an opening in a device comprising: filling at least a portion ofsaid passageway and said interconnects in the device of claim 1 with aliquid material; opening said passageway in at least one location,wherein said liquid material flows from said opening and substantiallycloses said opening.
 42. The method of claim 41, wherein said liquidmaterial cures after flowing from said opening.
 43. A method of mixing afluid, comprising passing a liquid through at least a portion of saidpassageway and said interconnects in the device of claim
 1. 44. Themethod of claim 43, wherein said liquid comprises a dissolved orsuspended solid.
 45. The method of claim 44, wherein said solid isselected from the group consisting of biomolecules, DNA, RNA, proteins,organic materials, inorganic materials, and combinations thereof.
 46. Amethod of directing at least one fluid to at least one portion of thedevice of claim 1, comprising: selectively sealing a portion of saidpassageway and said interconnects in the device of claim 1; introducingat least one fluid to at least one unsealed portion of said passagewayand said interconnects.
 47. The method of claim 46, wherein said hostfurther comprises electrodes that provide an electric potential todirect the at least one fluid.
 48. A host comprising a hollow passagewaydefined in the host, the passageway comprising a first substantiallytubular section aligned in a first plane in fluid communication with asecond substantially tubular section aligned in a second plane, whereinthe substantially tubular sections have a diameter of from 0.1 micron to1000 microns and the first plane and the second plane are substantiallyparallel.
 49. The host of claim 48, further comprising a plurality ofinterconnects that provide said fluid communication between said firstand second substantially tubular sections.
 50. The host of claim 48,wherein the passageway further comprises a third substantially tubularsection aligned in a third plane parallel to the second plane and influid communication with the second section.
 51. The host of claim 50,further comprising a plurality of interconnects that provide said fluidcommunication between said first, second, and third substantiallytubular sections.
 52. A host comprising a plurality of hollowpassageways defined therein, said passageways having a diameter of from0.1 micron to 1000 microns and having portions that are substantiallytubular, wherein said passageways are aligned in at least one commonplane and each of said passageways intersect with at least one otherpassageway in the said common plane.
 53. The host of claim 52, whereinthe substantially tubular portions of the passageways comprise at leasthalf the cross-sectional periphery of the passageways.
 54. In amicrostructure comprising a host material having a plurality ofpassageways aligned in a plurality of layers, at least one of saidpassageways in one layer in fluid communication with at least one ofsaid passageways in an adjacent layer, the improvement comprising: saidpassageways are substantially tubular and have an average diameter offrom 0.1 micron to 1000 microns.
 55. A microstructure comprising a hosthaving a three-dimensional grid of substantially tubular hollowpassageways defined therein, where each substantially tubular hollowpassageway has a diameter less than 1000 microns and is aligned in oneof a series of stacked parallel planes, at least one passageway in eachplane being connected to at least one passageway in an adjacent plane.56. The microstructure of claim 55, wherein the passageways in one planeare connected by a plurality of perpendicular interconnects to thepassageways in the adjacent parallel plane.
 57. The microstructure ofclaim 55, further comprising a cured resin that partially seals saidpassageways and said interconnects, such that a non-sealed portion ofsaid passageways and interconnects is in fluid communication to define avertically-oriented, square-spiral mixing tower.
 58. The microstructureof claim 55, further comprising a cured resin that partially seals saidpassageways and said interconnects, such that a non-sealed portion ofsaid passageways and interconnects is in fluid communication to define avertically-oriented, triangular-spiral mixing tower.
 59. Themicrostructure of claim 55, further comprising a cured resin thatpartially seals said passageways and said interconnects, such that anon-sealed portion of said passageways and interconnects is in fluidcommunication to define a twisted-pipe.
 60. A method of forming amicrocapillary network in a host comprising: providing a substrate;applying a fugitive material to a surface of said substrate to form asubstantially tubular filament, wherein said filament has an averagediameter of from 0.1 micron to 1000 microns; applying a host material tosaid substrate that encapsulates at least a portion of said filaments;curing said host material to form a host; removing at least a portion ofsaid fugitive material from the host to form a network of hollow,substantially tubular passageways in said host.
 61. The method of claim60, wherein said filament has an average diameter of from 10 microns to500 microns.
 62. The method of claim 60, wherein said filament has anaverage diameter of from 50 microns to 250 microns.
 63. The method ofclaim 60, wherein said filament forms a scaffold.
 64. The method ofclaim 63, wherein said scaffold is a three-dimensional scaffold.
 65. Themethod of claim 60, wherein said filament is first applied to saidsubstrate, said host material is then applied to said substrate toencapsulate at least a portion of said filaments, and said host materialis then cured.
 66. The method of claim 60, wherein said host material isfirst applied to said substrate as a liquid, said filament is thenapplied to said substrate, and said host material is then cured.
 67. Themethod of claim 60, wherein said substrate is selected from the groupconsisting of glass, plastic, metal, and combinations thereof.
 68. Themethod of claim 60, wherein said filament is applied to said substrateby forcing said fugitive material through an orifice.
 69. The method ofclaim 68, wherein said orifice has a diameter larger than the averagediameter of the filament.
 70. The method of claim 68, wherein saidfugitive material self-assembles after passing through said orifice. 71.The method of claim 60, wherein said filament is deposited on saidsubstrate by a computer controlled device comprising an orifice.
 72. Themethod of claim 71, wherein said computer controlled device is arobotically controlled deposition machine.
 73. The method of claim 60,wherein said fugitive material is heated prior to removal.
 74. Themethod of claim 60, wherein said fugitive material is removed by vacuum.75. The method of claim 60, wherein said fugitive material is removed asa liquid.
 76. The method of claim 60, further comprising filling aportion of said passageway, a portion of said interconnects, or aportion of said passageway and a portion of said interconnects with acurable resin.
 77. The method of claim 76, wherein said curable resin isphotocurable.
 78. The method of claim 76, wherein said curable resin isa photocurable epoxy.
 79. The method of claim 76, further comprisingcuring at least a portion of said curable resin and substantiallyremoving uncured curable resin.
 80. A method of forming a hostcomprising at least one substantially tubular, hollow passageway havinga first portion connected to at least a second portion by a plurality ofhollow interconnects, wherein said passageway has an average diameterfrom 0.1 micron to 1000 microns, the method comprising removing afugitive material from said host to form said hollow passageway and saidplurality of hollow interconnects.
 81. The method of claim 80, whereinsaid fugitive material is substantially removed as a liquid.
 82. Themethod of claim 80, wherein said fugitive material comprises at least80% nonvolatile components by weight.
 83. The method of claim 82,wherein said fugitive material comprises organic and inorganicconstituents.
 84. The method of claim 82, wherein said fugitive materialcomprises a majority of organic constituents.
 85. The method of claim82, wherein said fugitive material comprises a viscosity modifier. 86.The method of claim 82, wherein said fugitive material comprises lessthan 10% by weight of a viscosity modifier.
 87. The method of claim 85,wherein said viscosity modifier is selected from the group consisting ofporous colloid particles, calcium complex rods, lithium hydroxystearatefibers, liquid crystals, viscoelastic micelles, oligomers, beads,microcapsules, polymer fibers, ceramic fibers, metal fibers, andmixtures thereof.
 88. The method of claim 85, wherein said viscositymodifier comprises fumed silica.